Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium

Abstract

A study on transient free convection flow of a dusty viscous fluid through a porous medium is important for improving the existing industrial processes and for developing new chemical and geothermal systems. This paper presents a mathematical model for transient laminar free convective flow of a dusty viscous fluid through a porous medium in the presence of viscous energy dissipation. The partial differential equations governing the phenomenon were non-dimensionalized using some dimensionless quantities. The dimensionless coupled non-linear partial differential equations were solved using harmonic solution technique. The result obtained were presented graphically and discussed. These results revealed that increase in Peclet number, Eckert number and Grashof number leads to increase in the velocity profile. Increase in the mass concentration of the dust particles, concentration resistance ratio, Eckert number and Peclet number leads to increase in the velocity profile of the dust particles. Increase in the Reynold number leads to a reduction in the velocity profile. Increase in Peclet number, Eckert number and Grashof number leads to increase in temperature profile. Similarly, increase in heat source parameter, coefficient of Grashof number and Reynold number lead to reduction in the temperature profile.

Keywords

• Viscous energy dissipation;
• Harmonic solution;
• Grashof number;
• Eckert number